Lasius alienus and pallitarsis will found colonies before hibernation.

The bulk of Lasius Americanus fly in the summer so of course, they lay eggs well before hibernation. As previously stated it's only the late flying Lasius that doesn't lay eggs before hibernation. Of course, if you have records with pictures that say otherwise please share them with us.

An ants' strength can be rivaled by few animals compared to relative body size.

From my own experience (in Ireland) it really depends on a mixture of flight times, species and keeper.

Times are obvious.
Species take the cake here mostly as some are known to wait a some even forge for them selves and then wait until after winter when there is less risk to loose a lot of brood. Know your species and their habits.
Keepers!: We can also have a big factor on how long/ soon it will take a queen to lay eggs. If left under normal temperatures and left in the dark. The queen will lay eggs at the same.rate as in the wild.
I queen in a slightly colder area will lay eggs showly or not at all.
Now with controlled heat added to the equation a queen will lay eggs are a higher rate and brood will also develop faster as long as your careful with temperature regulation.
My Rubra is an example of this. I've read from a lot of people that their Rubra queen's waited until after winter to lay eggs because the flew in September as did mine. However with a lot of attention (not disruption as that is stress) and consistent temperature monitoring my queen had a healthy worker help her prepare for hybernation. Also hybernation times are not 100% accurate and thanks to this fact you can delay it by a week to give pupae a change to eclose. Just give them an extra few days hibernation to make up for this week or two.

But yeah even my latest Lasius flyer still had 2 workers before hibernation time came in. They grow like wild fire.

I am looking at my answer thinking "god, bet no one missed my replies on this forum xD"

Research is important before during and even after you have established a colony. There is always time to learn and to listen to others experiences. Live by this and your ants will thrive. Fail to do so and your experience may be brief.